The Quality of Experience (QoE) of streaming service is often degraded by frequent play-back interruptions. To mitigate the interruptions, the media player prefetches streaming contents before starting playback, at a cost of initial delay. We study the QoE of streaming from the perspective of flow dynamics. Firstly, a framework is developed for QoE when streaming users join the network randomly and leave after downloading completion. We model the distribution of prefetching delay using partial differential equations (PDEs), and the probability generating function of playout buffer starvations using ordinary differential equations (ODEs) for constant bit-rate (CBR) streaming. The explicit form starvation probabilities and mean start-up delay are obtained by use of a matrix function approach. Secondly, we extend our framework to characterize the throughput variation caused by opportunistic scheduling at the base station, and the playback variation of variable bit-rate (VBR) streaming. Our study reveals that the flow dynamics is the fundamental reason of playback starvation. The QoE of streaming service is dominated by the first moments such as the average throughput of opportunistic scheduling and the mean playback rate. While the variances of throughput and playback rate have very limited impact on starvation behavior in practice.